Current treatment guidelines call for aggressive treatment of cholesterol levels in patients with clinically evident atherosclerotic disease. However, there is a little data about coronary events once LDL (bad) cholesterol target levels are reached, and there is conflicting evidence about benefits conferred once LDL cholesterol levels are below the minimum target. The aim of this study is to determine whether there is additional benefit (reduced coronary heart disease risk) if LDL cholesterol levels are below the minimum currently recommended. In this trial atorvastatin will be used to lower cholesterol levels. Atorvastatin is a drug under extensive investigation and has been apporved for use in the United States for the treatment of high cholesterol. A total of 8,600 men and women worldwide will be enrolled in this trial. Patients must be between 35 and 75 years old and be at high risk of heart disease. High risk is defined as a prior myocardial infarction, angina, coronary revascularization or high LDL cholesterol level. Each subject will be in the trial for 5 years. It is hoped that the information gathered in this study will help to optimize treatment strategies for patients at high risk for coronary heart disease.